# Finding multinomial logistic regression coefficients using Solver

The approach described in Finding Multinomial Logistic Regression Coefficients doesn’t provide the best estimate of the regression coefficients. In fact a higher value of LL can be achieved using Solver.

Referring to Figure 2 of Finding Multinomial Logistic Regression Coefficients, set the initial values of the coefficients (range X6:Y8) to zeros and then select Data > Analysis|Solver and fill in the dialog box that appears with the values shown in Figure 1 (see Goal Seeking and Solver for more details) and then  click on the Solve button.

Figure 1 – Solver dialog box for Multinomial Logistic Regression

The result is displayed in Figure 2 and 3.

Figure 2 – Multinomial logistic regression model using Solver (part 1)

Figure 3 – Multinomial logistic regression model using Solver (part 2)

As you can see the value of LL calculated by Solver is -163.386 (see Figure 3), which is a little larger than the value of -170.269 calculated by the binary model (see Figure 4 of Finding Multinomial Logistic Regression Coefficients).

To test the significance of the coefficients (the equivalent of Figure 5 of Finding Multinomial Logistic Regression Coefficients for the Solver model) we need to calculate the covariance matrix (as described in Property 1 of Finding Multinomial Logistic Regression Coefficients). This is shown in Figure 4.

Figure 4 – Calculation of the Covariance Matrix

The covariance matrix displayed in Figure 4 is calculated using the formulas shown in Figure 5.

Figure 5 – Formulas used in Figure 4

Using the results in Figure 2 and 4, we get the result shown in Figure 6.

Figure 6 – Multinomial logistic regression model using Solver (part 3)

The key formulas used to calculate the Cured + Dead table are shown in Figure 7 (the Sick + Dead table is similar).

Figure 7 – Key formulas in Figure 6

The forecasted probabilities, based on the multinomial logistic regression model using Solver, of the three outcomes for men and women at a dosages of 24 mg and 24.5 mg is displayed in Figure 8.

Figure 8 – Forecasted probabilities using Solver

### 6 Responses to Finding multinomial logistic regression coefficients using Solver

1. Ed says:

I’ve been working with a political campaign and decided to try a logistic regression to get a rough predictive formula for the likelihood of an individual voter showing up to the polls. My LL seems really low though, around -12,000. is this something that would indicate I did something wrong?

• Charles says:

Ed,
The value of LL really depends on the nature of your data, and doesn’t necessarily mean that you have done something wrong.
Charles

2. Anson says:

Hi Charles,

As per your above samples, how can I find the p value of dead?

Anson

• Charles says:

Anson,
There probably is a way to do this based on the analysis already done, but I can’t think of it at this moment. Instead, you can reanalyze the original data taking one of the other variables (e.g. Gender) and the base variable.
Charles

3. ed says:

is there any way you could post the spreadsheet you are using so that some of the values and where they came from are more clear? thanks,